State-generating matrix for differential Mueller matrices of depolarizing optical media

Unlike the Mueller matrix, where parameters are not directly accessible for physical interpretation, the state-generating matrix recently introduced [J. Opt. Soc. Am. A34, 80 (2017)JOAOD60740-323210.1364/JOSAA.34.000080] provides a powerful mathematical tool for formulating all properties of nondepolarizing systems. Extending this notion to the case of depolarizing differential Mueller matrices is the issue we address in this paper. We show that the formulation of the problem using complex random vectors makes it possible to directly introduce the formalism of a state-generating matrix in the case of differential depolarizing matrices. Examples of physical interpretations that can be obtained are presented specifically for a homogeneous medium. Illustrations are given when the complex vector degenerates into a complex scalar and when a Gaussian random processes hypothesis is made.